M lefranc, S. Boccaletti, B. Gluckman, C. Grebogi, J. K¨ Urths, L. Pecora

11

2

3Department of Physics, University of Michigan, Ann Arbor, USA

Department of Neurology, University of Michigan Medical School, Ann Arbor, USA

1

9Tel Aviv University, Tel Aviv, Israel [e-mail]

In many cases interacting networks are adaptive system themselves, that undergo constant reorganization. The brain is a prime example of such a system. In this case the network reorganization not only consists of reorganization of network connectivity but may also include addition of new network nodes and deletion of existing ones. In hippocampal formation, new neurons are generated throughout life and integrate into the network via the process of adult neurogenesis. This process is thought to have an important functional role in healthy networks, but also may lead to pathological structural changes in epileptic brain. What controls this neural augmentation remains unknown. We use computational simulations to investigate the effect of network environment on structural and functional outcomes of neurogenesis. We find that small-world networks with external stimulus are able to be augmented by activity-seeking neurons in a manner that enhances activity at the stimulated sites without altering the network properties as a whole. However, when inhibition is decreased or connectivity patterns are changed, new cells are both less responsive to stimulus and the new cells are more likely to drive the network into bursting dynamics. These patterns are being compared with the experimental ones observed in a culture system

.

Tidal instability in exoplanetary systems

David C ´ ebron1, Rim Far ` es2, Michael Le Bars1, Pierre Maubert1, Claire Moutou2, & Patrice Le Gal

11Institut de Recherche sur les Ph ´ enom ` enes Hors Equilibre

2Laboratoire d’Astrophysique de Marseille [e-mail]

Due to their observationnal method, many of the discovered exoplanets are massive gas giants called ’hot Jupiters’ orbiting rapidly very close to their stars. Because of this proximity, these binary bodies (stars and planets) are strongly deformed by gravitationnal tides. Therefore, a certain number of them must be the site of an hydrodynamic instability, called the tidal instability. Starting from measured astrophysical characteristics of these systems (masses, orbit radius, eccentricity and period, spin velocity...), we show that this instability is, as expected, present in some of the stars when the ratio of the planet orbiting period to the star spinning period is not in a ”forbidden range”. In this case, the instability should drive strong flows in the different fluid layers of both bodies. These flows must be taken into account to model the binaries interiors and subsequent properties (synchronization, dynamos, zonal winds...). Of particular interest is the possibility of modifying the alignment of the rotation axes of stars and planets by this tidal instability.

2

0

Spectral analysis of interannual bed level variations at a beach in Duck, North Carolina, USA

Vanesa Magar1, Dominic Reeve1, Marc Lefranc2, & Rebecca Hoyle

31

2

3School of Marine Science and Engineering, University of Plymouth, UK

Phlam and CERLA, Universit ´ e des Sciences et Technologies de Lille, France

2

1Department of Mathematics, University of Surrey, UK [e-mail]

The nearshore dynamics of a sandbarred beach at Duck, N.C., U.S.A., surveyed monthly for 26 years, is analysed using spectral methods and recurrence plots. The first part of the study focused on two shore-normal bathymetric profiles at locations where the beach is quasi longshore uniform. A singular spectrum analysis (SSA) permitted the identification of the fundamental, dominant frequencies of oscillation. The identification of interannual quasi-periodic cycles of varying periodicities at different locations along the profile led to the characterisation of bathymetric regions based on the properties of the local quasi-periodic oscillations. Yearly and quasi-yearly cycles were linked to the monthly averaged wave conditions, and some regime changes observed in the temporal behaviour agreed well with observations of sandbar configuration changes and sandbar dynamics. In these cases such changes could generally be associated to extreme storm events, as found by previous authors. Some of the interannual patterns may be associated with the North Atlantic Oscillation.

The second part of the study concentrated on an in-depth investigation of coherent temporal patterns and their likely origin. It is shown that these patterns are linked to large-scale phenomena using a multivariate EOF (MEOF) analysis and a Multichannel SSA (MSSA). These methods were applied to the whole bathymetry and to three potentially important monthly forcings: the North Atlantic Oscillation (NAO), the monthly wave height (MWH) and the monthly mean water level (MWL). Even though no interannual coherent patterns were found, a few at monthly timescales were identified. Of these, the yearly and semi-yearly patterns forced by the MWH were clearly dominant, followed by a few patterns at shorter timescales linked to the NAO

.

Bouncing trimer, bouncing droplet: bouncing modes

St ´ ephane Dorbolo1, Nicolas Vandewalle1, Denis Terwagne1, Franc¸ois Ludewig1, & Tristan Gilet

21

2GRASP-D ´ epartement de Physique- Universit ´ e de Li ` ege

2

2Mathematic department-MIT-Boston-USA [e-mail]

The bouncing ball on a vibrating surface is among the simplest systems that exhibit chaotic features. This problem involves non linear behaviours such as period doubling, orbits, and transition to chaos, that are still far from being exhaustively investigated. The bouncing ball is often considered as a point particle, and we may wonder how a more complex item bounces on the vibrating surface. This communication presents some experiments in which degrees of freedom are progressively added to the bouncing item. First, we have studied objects constituted by two or three linked centimetrical beads (they are called dimer and trimer), that may translate and rotate. Then, we introduced the deformation by studying the dynamics of a bouncing droplet on a high viscous silicone oil bath. In both cases, exotic bouncing modes can be observed: self-propulsion for dimer, rotation and period-3 for trimer, rolling droplets, double emulsification,... Experimental and simulation movies will be shown for both studies

.

Transition dynamics of structural motifs in a granular contact network

David Walker1, Antoinette Tordesillas1, Gary Froyland2, & Robert Behringer

31

2

3Department of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3010 Australia

School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052 Australia

2

3Department of Physics, Duke University, Durham, NC 27708 USA [e-mail]

A deforming dense assembly of granular particles can be usefully represented by its evolving contact network. A study of the 3-cycle motifs of the contact network and their interplay with the force chains of structural mechanics reveals that in an effort to ward off imminent failure a granular material rearranges to form structures akin to the power towers seen in theme parks. A more detailed investigation of other network motifs, in particular their transition dynamics, uncovers the most prevalent and almost-invariant transition sets of motifs within the material. When further coupled, at the meso-scopic scale, to a measure of structural stability we begin to probe the role these granular motifs play in the self-organization properties and preferred configurations apparent in a granular material subject to loading. Results are presented for an experimental biaxial apparatus of bi-disperse photo-elastic disks subject to pure shear

.

Characterising time series dynamics with complex networks

Michael Small1, Ruoxi Xiang1, Jie Zhang1, & Xiaoke Xu1;

21

2Department of Electronic and Information Engineering, Hong Kong Polytechnic University

2

4School of Communication and Electronic Engineering, Qingdao Technological University, Qingdao 266520, China [e-mail]

The application of complex network structure for the analysis of time series has recently led to several new approaches to quantify dynamical behaviour in nonlinear systems. In general these methods construct some sort of network from the time series by mapping dynamical states in the underlying system to individual nodes and drawing links between similar nodes. In particular, one of these methods* has shown considerable promise by providing a classification for dynamical behaviour. By measuring the relative frequency of occurrence of different motifs this method has been shown to be able to differentiate between low-dimensional chaos (one positive Lyapunov exponent), hyper chaos, periodic, quasi-periodic and noise periodic dynamics.

By applying this method to nonlinear time series models we show how this method can be extended to short and noisy time series, and can be used to both evaluate and qualitatively describe the performance of these models. We build nonlinear models (we use a radial basis model structure, but the choice is arbitrary) from time series data and then evaluate features of the complex networks structures for time series simulations produced by these models and for the original data. In cases were the original data was sufficient to make a meaningful assessment of the network structure we can determine which models are qualitatively good models. In cases were the original data is insufficient we can use the performance of the models as a surrogate and make a meaningful estimate of the various possible alternatives.

We apply the method to a short ecological time series and an ensemble of long time series of sustained musical tones. For the ecological time series (annual populations of Canadian Lynx) we find the previous pronouncements of chaos in this system are premature. For the tone data (pure tones on a standard B[clarinet) we show strong evidence for bounded aperiodic dynamics which is not consistent with low-dimensional chaos. Further support for this conclusion can be obtained from surrogate time series methods and some of the more usual nonlinear time series measures. We also observe that (for the clarinet data) the models with the “right” dynamics are also the models that sound “right”.

*X. Xu, J. Zhang and M. Small. “Superfamily phenomena and motifs of networks induced from time series.” Proceedings of the National Academy of Sciences of the United States of America 105 (2008): 19601-196

0

Consequences of violated simultaneity on the concept of causality

Linda Sommerlade1;2;3, Jens Timmer1;2;3;4, & Bj ¨ orn Schelter1;2;

31

2

3

4Department of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany

Bernstein Center for Computational Neuroscience, University of Freiburg, Hansastr. 9A, 79104 Freiburg, Germany

FDM, Freiburg Center for Data Analysis and Modeling, University of Freiburg, Eckerstr. 1, 79104 Freiburg, Germany

2

5Freiburg Institute for Advanced Studies, Albertstr. 19, 79104 Freiburg, Germany [e-mail]

Inferring causal interaction structures in networks of dynamical processes is of particular interest in neurosciences. Since simultaneity of measurements cannot be guaranteed, we investigate its implications for causality, in particular Granger-causality based partial directed coherence, applied to linear and non-linear systems. We present three situations in which the na ¨ ive application of partial directed coherence leads to misleading results. We discuss possible solutions to this end. We also address the question how Granger-causality can be applied to measured data in this context

.

Reduction of the complexity of an open cavity air-flow by catching the spatial flow organization within a few dynamical modes

Luc Pastur1;2, Franc¸ois Lusseyran1, J ´ er ´ emy Basley1;2, & Nathalie Delprat1;

31

2LIMSI-CNRS

Universit ´ e Paris Sud 1

13Universit ´ e Pierre et Marie Curie [e-mail]

Most open systems in fluid dynamics potentially own an infinite number of degrees of freedom, which makes questionable approaches in terms of dynamical system analysis. However, in many situations, the flow complexity actually reduces to very coherent features together with few characteristic structures in space and time, suggesting that the actual number of degrees of freedom is small. The resulting flow organization, therefore, can often be considered as the projection of the full dynamics over some central variety, whose dimension is small, such that a few modes may be selected as relevant with respect to the long-time dynamics (associated to vanishing or close to imaginary eigenvalues), all the other modes being slaved to them. In a very recent work, Schmid and Sesterhenn (2008) have shown how to compute modes relevant with respect to the non-linear state evolution of such systems. The method is empiric, the mode computation being directly done based on successive, time-resolved, realizations of some observable (velocity field, pressure, etc), without any explicit knowledge of the evolution-operator (which may be by the Navier-Stokes equation). The resulting modes of the decomposition are called ”dynamical modes” by Schmid and Sesterhenn because they are the eigen-modes of some operator-evolution in the functional space of the observable acting on the fully non-linear state. In the limit of infinite horizon time, beyond transient phenomena, when the dynamics evolves on an attractor, the dynamical modes reduce to the Koopman modes, which are well-estimated by the discrete (time) Fourier transformed (spatial) modes, as shown by Rowley et al (2009). Based on this assumption, we have identified the dynamical modes characteristic of an experimental cavity air-flow. The cavity is rectangular and the flow incompressible (low Mach number limit), which is an academic configuration for studying self-oscillating flows. Such flows are known to exhibit narrow-banded power spectra, due to the enhancement of self-sustaining oscillations. In such strongly organized flows, dynamical or Koopman modes provide an efficient way for reducing the flow complexity, for they catch the spatial structures characteristic of the flow with respect to its space-time dynamics.

Bibliography

Schmid and Sesterhenn (2008), Schmid P. and Sesterhenn J., (2008) ”Dynamic mode decomposition of numerical and experimental data”, Sixty-First Annual Meeting of the APS Division of Fluid Dynamics, San Antonio, Texas, USA.

Rowley et al (2009), Rowley C. W., Mezic I., Bagheri S.,Schlatter P. and Henningson D. S. (2009) ”Spectral analysis of nonlinear flows”, Journal of Fluid Mechanics, pp. 1-13

2

6

Time series analysis of an pH oscillatory chemical reaction

Igor Schreiber1, Daniel Bakes1, Lenka Schreiberova1, & Marcus Hauser

21

2Institute of Chemical Technology, Prague, Department of Chemical Engineering, Technicka 5, 166 28 Prague 6, Czech Republic

2

7Otto-von-Guericke Universitat Magdeburg, Institut f ¨ ur Experimentelle Physik, Universit ¨ atsplatz 2, Magdeburg, Germany [e-mail]

We examine transition from periodic to chaotic oscillations experimentally observed in the continuous stirred tank reactor with the reaction of hydrogen peroxide, thiosulfate and sulfite in weakly acidic environment (HPTS) and presence of carbon dioxide. The HPTS reaction is an pH oscillator signifying that the hydrogen ions take part in the autocatalysis. Mixed-mode oscillations and chaos have been observed earlier but no detailed quantitative analysis of the degree of chaoticity were determined. The reaction is sensitive to the presence of carbon dioxide and a controlled inflow of this reactant has been chosen as the bifurcation parameter.

The measured time series of pH indicate simple periodic oscillations, mixed-mode oscillations of various degree of complexity and apparently chaotic oscillations with no distinct separation of amplitudes. We use SVDbased methods for reconstruction of phase portrait, noise reduction and determination of embedding dimension. There seem to be a few dozens of modes involved in building up the attractor and its geometry appears quite complex. We also calculate maximum Lyapunov exponent, which turns to positive values as the periodic mixed-mode regime transforms into chaos.

Building on an early version of a mechanism of this complex chemical reaction, we present an extended version and discuss its potential for reproducing the experiments using an approach based on stoichiometric network analysis

.

Biological algorithm for data reconstruction

Robert Gilmore, Daniel Cross, & Ryan Michaluk

Department of Physics, 3141 Chestnut St, Philadelphia, PA 19104 [e-mail]

1We present a simple algorithm inspired by Genome sequencing which “reconstructs” a single long trajectory of a dynamical system from many short trajectories2. Such a procedure would be useful in situations where many data sets are available but each is insufficiently long to apply a meaningful analysis directly. We apply the algorithm to numerical data taken from the R ¨ ossler and Lorenz dynamical systems and to experimental data taken from the Belousov-Zhabotinskii chemical reaction. Topological information was reliably extracted from each system and geometrical and dynamical measures were computed.

1. C. Komalapriya, M. Thiel, M. C. Romano, N. Marwan, U. Schwarz, and J. Kurths, Phys. Rev. E 78, 066217 (2008).

2. D. J. Cross, R. Michaluk, and R. Gilmore, Phys. Rev. E, in press (2010).

2

8

Arbitrary order Hilbert spectral analysis : a new tool to analyze the scaling complexity of time series, application to turbulence data

Francois Schmitt1, Yongxiang Huang1;2, Zhiming Lu2, & Yulu Liu

21

2Laboratory of Oceanology and Geosciences, CNRS-University of Lille 1, France

Refs: Huang Y., F. G. Schmitt, Z. Lu, Y. Liu, EPL 84, 40010, 2008 Huang Y., F. G. Schmitt, Z. Lu, Y. Liu, EPL 86, 40010, 2009 Schmitt FG, Y Huang, Z. Lu, Y. Liu, N. Fernandez, Journal of Marine Systems 77, 473-481, 2009 Huang Y., F. G. Schmitt, Z. Lu, Y. Liu, Journal of Hydrology 373, 103-111, 2009

2

9Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, China [e-mail]

Empirical Mode Decomposition (EMD) is an analysis technique introduced by Norden Huang in 1998; it was imagined to decompose a complex time series into a sum of modes, each one being narrrow banded. This method is fully data-driven, and is suitable for nonlinear and nonstationary time series. Since its introduction this method has been applied in more than 1000 papers, in many fields of natural sciences including oceanic and atmospheric sciences, climate studies, mechanical engineering, biomedical and biological sciences, among others. It has been completed by Hilbert Spectral Analaysis (HSA), a method involving Hilbert transform to characterize time series fluctuations in an amplitude-frequency space.

Here we generalize this approach in order to characterize the scaling intermittency of complex time series in an amplitude-frequency space. The new method is a arbitrary order Hilbert spectral analysis. As a first step the method is applied to fractional Brownian motion, and then to homogeneous turbulence data and chaotic and nonlinear signals.

We show that Hilbert spectral analysis can be used to recover the Kolmogorov -5/3 inertial range; we obtain a 2D amplitude-frequency representation of the pdf p(A;!) of turbulent fluctuations with scaling trend. We obtain multifractal scaling exponents in amplitude-frequency space and show that they are close to the ones in real space, despite the quite different approaches used in both cases. We find that the new methodology provides a better estimator than the classical structure functions.

We then investigate the effect of a periodic component on both structure functions and the Hilbert approach, and find that the former one is strongly influenced by the periodic component, whereas the latter can constrain such effect in an amplitude-frequency space. This shows the usefulness of this new method for general scaling processes and especially for time series possessing energetic large scales.

This new approach is able to characterize the multi-scale properties of the fluctuations of nonlinear time series. It is likely to have many different applications for data analysis of nonlinear, chaotic and complex time series

.

Advances with nonlinear nanoelectromechanical systems (NEMS)

Rassul KARABALIN

Kavli Nanoscience Institute and Department of Physics, California Institute of Technology, Pasadena, CA, USA

The emerging field of NEMS has recently spawned an exceptional growth of interest amongst research and engineering communities. In ongoing efforts it has been quickly discovered that these tiny mechanical structures, among their other remarkable attributes, possess very strong and easily attainable nonlinear characteristics. Along with the high attainable frequencies and precisely controllable major parameters of NEMS, it is now readily apparent that their nonlinear properties provide unprecedented opportunities. Among the most exciting are attaining substantial improvement in the performance of NEMS-enabled applications, and the use of coherently-coupled NEMS arrays, as an exceptional ”playground” for experimental studies of complex nonlinear dynamics. In this talk I will review some of the remarkable advances made in the past decade with nonlinear NEMS. Parametric resonance is one of the most important examples of a useful nonlinear-enabled physical phenomenon. We have demonstrated various novel nanomechanical implementations this phenomenon. The most straightforward is parametric mechanical amplification, providing high linear gain and very substantial quality factor enhancement. Beyond such practical applications, parametric effects enable realization of new types of nonlinear system with nontrivial dynamical properties. Phenomena such as wide hysteresis and precisely controllable bifurcations can be observed and investigated in detail. Further, the ability to excite motion using only parametric pumping enables us to build self-sustained nonlinear oscillators manifesting unexpected properties.